Gymnast Clothing manufactures expensive hockey jerseys for sale to college books

Question

Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 300. Its cost (in dollars) for a run of x hockey jerseys is

The hourly operating cost of a plane which seats up to 405 passengers is estimated to be $5,283. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. HINT [The cost function is constant (Variable cost = 0).]

P(x) = Gymnast Clothing manufactures expensive hockey jerseys for sale to college bookstores in runs of up to 300. Its cost (in dollars) for a run of x hockey jerseys is C(x) = 3000 + 10x + 0.2x2 (0 ? x ? 300) Gymnast Clothing sells the jerseys at $105 each. Find the revenue function. Find the profit function. How many should Gymnast Clothing manufacture to make a profit? HINT [See Example 2.] (Round your answer up to the nearest whole number.) jerseys The hourly operating cost of a plane which seats up to 405 passengers is estimated to be $5,283. If an airline charges each passenger a fare of $100 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. HINT [The cost function is constant (Variable cost = 0).] Specify the domain. [0, 405](?5283, 5283) (100, 405)[0, 100][?405, 405] What is the least number of passengers the plane must carry in order to make a profit? (Round your answer up to the nearest whole number.)

Explanation / Answer

revenue function = 105*x

profit function = 105x-3000 + 10x + 0.2x2=95x -3000- 0.2x2

=95x -3000- 0.2x2>0

x>34

so 34

hourly profit P= 100x-5,283

domain [0, 405]

100x-5283>0

so 53 passengers

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